Cosmology of spin-2 fields
The Cauchy-Kowalevski theorem is applied to the solutions of Einstein’s equations and to cosmology. Three fundamental requirements of the theorem: the use of analytic series; the existence of the boundary surfaces; and the setting of the independent initial data are revised, using methods of geometric analysis. It is found that during its relativistic phase the standard model of the universe is completely governed by Einstein’s gravitation, in which the source includes a massive spin-2 field, compatible with the observations of the dark sector of the universe. On the other hand, the exponential growth of the volume of the universe at the inflationary phase, is shown to be predominantly thermodynamical, as opposed to a relativistic process. These two phases are joined by the last inflationary surface endowed with a mirror symmetry, which eventually suggests a possible bouncing universe scenario.